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Unformatted text preview: Show using a Galerkin method truncated to the lowest order modes, that the square state in Problem 1 is stable (you only need to consider perturbations which correspond to the growth or decay of one set of stripes relative to the other). Next show that the stripe state is unstable towards the growth of an orthogonal set of stripes (cross-roll instability), i.e., the stripe state is unstable towards squares. Problem 3 Eckhaus instability. Calculate the stability of the stripe solutions to the Swift-Hohenberg equation near onset to a longitudingal perturbation in the one mode approximation, following the method we used in class to consider the stability with respect to transverse perturbations (zigzag instability)....
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